Geodesic
Longitudinal waves in an elastic rod caused by sudden damage to the foundation
Theoretical and applied mechanics, Tome 48 (2021) no. 1.

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We study the problem of propagating longitudinal waves in an elastic rod connected to a locally damaged foundation through a thin elastic layer. The motion of the rigid foundation blocks is considered predetermined. We formulated the initial-boundary problem for the Klein--Gordon equation with a discontinuous right-hand side. The nonstationary fields of displacements, velocities, and deformations were investigated by the Laplace integral transformation method. Examples of sudden divergence of fragments of the foundation by a given value and their mutual separation at a constant speed are considered.
Keywords: elastic rod, thin layer, damaged foundation, dynamics, longitudinal wave 
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     author = {Ivan Shatskyi and Vasyl Perepichka and Maksym Vaskovskyi},
     title = {Longitudinal waves in an elastic rod caused by sudden damage to the foundation},
     journal = {Theoretical and applied mechanics},
     pages = {29 - 37},
     publisher = {mathdoc},
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     number = {1},
     year = {2021},
     url = {http://geodesic.mathdoc.fr/item/TAM_2021_48_1_a1/}
}
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Ivan Shatskyi; Vasyl Perepichka; Maksym Vaskovskyi. Longitudinal waves in an elastic rod caused by sudden damage to the foundation. Theoretical and applied mechanics, Tome 48 (2021) no. 1. http://geodesic.mathdoc.fr/item/TAM_2021_48_1_a1/